2-strict convexity and continuity of set-valued metric generalized inverse in Banach spaces
type: Item
instance of: scholarly article
title: 2-strict convexity and continuity of set-valued metric generalized inverse in Banach spaces
zbMATH Open document ID: 1472.47002
DOI: 10.1155/2014/384639
author: Shaoqiang Shang
author: Yunan Cui
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Authors investigate the metric generalized inverses of linear operators in Banach spaces. Authors prove by the methods of geometry of Banach spaces that, if \(X\) is approximately compact and \(X\) is 2-strictly convex, then metric generalized inverses of bounded linear operators in \(X\) are upper semicontinuous. Moreover, authors also give criteria for metric generalized inverses of bounded linear operators to be lower semicontinuous. Finally, a sufficient condition for set-valued mapping \(T^\partial\) to be continuous mapping is given.
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A06
zbMATH DE Number: 7022278
zbMATH Keywords: metric generalized inverses
zbMATH Keywords: upper semicontinuous
zbMATH Keywords: lower semicontinuity
Wikidata QID: Q59037043
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/384639
OpenAlex ID: W2086309262
cites work: An Introduction to Banach Space Theory
cites work: Q3286569
cites work: Set-valued analysis
cites work: Approximative compactness and continuity of metric projector in Banach spaces and applications
cites work: Q3213666
cites work: Nearly dentability and approximative compactness and continuity of metric projector in Banach spaces
cites work: A Generalization of Uniformly Rotund Banach Spaces
cites work: Q4730294
cites work: A unified approach to generalized inverses of linear operators: I. Algebraic, topological and projectional properties
cites work: Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces
cites work: Perturbation analysis of generalized inverses of linear operators in Banach spaces
cites work: Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces
cites work: Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces
cites work: Criteria for the metric generalized inverse and its selections in Banach spaces
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description: scientific article; zbMATH DE number 7022278